Inventing saw allows tribe to gain double amount of wood from trees. Saw has no requirements to unlock, and is available early in the game. If you constantly find yourself low on wood, saw is a good upgrade for you.
Saw is nice to have if you need wood, because it frees up a minion who otherwise would have an axe. If you don't use lumberjacks at all in the endgame, it's probably smarter not to spend an upgrade on saw and focus on combat upgrades instead.